Crystallization of amorphous multicomponent ionic compounds

ABSTRACT

A method for crystallizing an amorphous multicomponent ionic compound comprises applying an external stimulus to a layer of an amorphous multicomponent ionic compound, the layer in contact with an amorphous surface of a deposition substrate at a first interface and optionally, the layer in contact with a crystalline surface at a second interface, wherein the external stimulus induces an amorphous-to-crystalline phase transformation, thereby crystallizing the layer to provide a crystalline multicomponent ionic compound, wherein the external stimulus and the crystallization are carried out at a temperature below the melting temperature of the amorphous multicomponent ionic compound. If the layer is in contact with the crystalline surface at the second interface, the temperature is further selected to achieve crystallization from the crystalline surface via solid phase epitaxial (SPE) growth without nucleation.

REFERENCE TO GOVERNMENT RIGHTS

This invention was made with government support under 1121288 awarded bythe National Science Foundation. The government has certain rights inthe invention.

BACKGROUND

Considerable effort has been devoted to the synthesis of crystallinecomplex oxides using methods that provide low defect densities whilesimultaneously providing control over the shape, crystallographicorientation and elemental composition of nanomaterials. The creation ofthin layers of oxide single-crystals largely employs epitaxial growthtechniques from the vapor phase, which relies on elevated surfacetemperatures to favor kinetic processes including long-range surfacediffusion. (D. G. Schlom, L. Q. Chen, X. Q. Pan, A. Schmehl, M. A.Zurbuchen, “A thin film approach to engineering functionality intooxides,” J. Am. Ceram. Soc. 91, 2429-2454 (2008) and J. L.MacManus-Driscoll, “Self-Assembled Heteroepitaxial Oxide NanocompositeThin Film Structures: Designing Interface-Induced Functionality inElectronic Materials,” Adv. Funct. Mater. 20, 2035-2045 (2010).) Growthvia epitaxial techniques based on elemental or chemical sources is,however, constrained to planar substrates by line-of-sight geometricconsiderations, yielding two-dimensional thin-film heterostructures.

The three-dimensional integration of complex oxide crystals in intricatenanoscale geometries can enable new applications of complex oxides inoxygen transport, in single crystal composites for the control ofthermal properties, and by yielding complex oxides in sufficient volumeor numbers of nanostructures in which mechanical, optical, andelectronic effects are modified by size effects.⁴⁻⁵ The promisingproperties of nanoscale complex oxide materials have been discovered andstudied at the scale of individual structures,⁶ but at present routes tothe areas on the order of square centimeters incorporating a largenumber of nanostructures required for applications are lacking. Inaddition, two-dimensional electron gases have potentially widespreadapplications in nanoscale geometries, but can presently be synthesizedonly in two-dimensional geometries in epitaxial systems based on complexoxide single-crystal substrates.^(7,8) Controlling the nucleation andgrowth of complex oxides, in sophisticated geometries, remains an openchallenge.

SUMMARY

Provided are methods for crystallizing amorphous multicomponent ioniccompounds (e.g., multicomponent oxides such as perovskite oxides,) whichhave been previously deposited on amorphous surfaces (e.g., a surface ofa plastic substrate), including in the form of intricate,three-dimensional structures.

In an embodiment, a method for crystallizing an amorphous multicomponentionic compound comprises applying an external stimulus to a layer of anamorphous multicomponent ionic compound, the layer in contact with anamorphous surface of a deposition substrate at a first interface.Optionally, the layer is in contact with a crystalline surface at asecond interface. The external stimulus induces anamorphous-to-crystalline phase transformation, thereby crystallizing thelayer to provide a crystalline multicomponent ionic compound. Theexternal stimulus and the crystallization are carried out at atemperature below the melting temperature of the amorphousmulticomponent ionic compound. If the layer is in contact with thecrystalline surface at the second interface, the temperature is furtherselected to achieve crystallization from the crystalline surface viasolid phase epitaxial (SPE) growth without nucleation.

The following is a non-exhaustive list of abbreviations used in thepresent disclosure: solid phase epitaxy (SPE), transmission electronmicroscope (TEM), X-ray reflectivity (XRR), two-dimensional electron(hole) gas (2DE(H)G).

Other principal features and advantages of the invention will becomeapparent to those skilled in the art upon review of the followingdrawings, the detailed description, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the invention will hereafter be describedwith reference to the accompanying drawings, wherein like numeralsdenote like elements.

FIG. 1 illustrates the thermodynamics of the different phases of silicon(Si). This graph was redrawn from J. Y. Tsao, Materials Fundamentals ofMolecular Beam Epitaxy, 1993.

FIG. 2A shows a side view of a schematic of a deposition substrateproviding a single region, an amorphous surface. FIG. 2B shows a sideview of a schematic of another deposition substrate providing aplurality of regions, including amorphous and crystalline surfaces.

FIG. 3 shows a side view of another deposition substrate providing aplurality of regions, including amorphous and crystalline surfaces. FIG.3 also illustrates crystallization of an amorphous layer via SPE growthon the deposition substrate.

FIGS. 4A-4D show a side view of another deposition substrate providing aplurality of regions, including amorphous and crystalline surfaces.FIGS. 4A-4D also illustrate the crystallization of an amorphous layervia SPE growth on the deposition substrate to form a complex,three-dimensional (3D) crystalline structure.

FIGS. 5A-5B shows schematic diagrams of the structural changes in theannealing process for (FIG. 5A) SrTiO₃ (STO) on (001) STO substrates bySPE and (FIG. 5B) STO on SiO₂/(001) Si substrates by nucleation andgrowth.

FIGS. 6A-6D show X-ray scattering patterns. FIG. 6A shows amorphous STOon (001) STO. FIG. 6B shows amorphous STO on SiO₂/(001) Si, with a ringof scattering from amorphous STO at a at 2θ angle of 29.5°. FIG. 6Cshows crystallized STO on (001) STO. FIG. 6D shows crystallized STO onSiO₂/(001) Si. Rings of powder diffraction intensity at 2θ angles of22.8°, 32.30, and 39.8° appear following crystallization on SiO₂/(001)Si.

FIG. 7A shows high-resolution TEM micrographs of fully crystallized STOfilms on (001) STO substrates. FIG. 7B shows high-resolution TEMmicrographs of fully crystallized STO films on SiO₂/(001) Si substrates.

FIG. 8A shows the amorphous phase X-ray scattered intensity as afunction of annealing time for STO layers annealed at temperatures of450° C., 550° C., 600° C. and 650° C. FIG. 8B shows growth velocitiesmeasured using the data shown in FIG. 8A (squares), and growth velocityat 600° C. determined using XRR (triangle).

FIG. 9 shows amorphous STO layer thickness, derived from the fringespacing in XRR data, as a function of annealing time at 600° C.

FIG. 10 shows the relationship between film thickness and density as afunction of annealing time at 600° C.

FIGS. 11A-11D show a comparison between amorphous phase scattered x-rayintensity between STO on SiO₂/(001) Si substrate and STO on (001) STOsubstrate, as a function of annealing time, at different annealingtemperatures. The nucleation delay for STO on SiO₂ becomes obvious atrelatively lower annealing temperatures.

FIG. 12A shows the thermally activated nucleation kinetics of STO onSiO₂/(001) Si substrates as a function of annealing temperature. FIG.12B shows the maximum STO film distance (L_(C)) achieved bycrystallization of amorphous STO phase on a STO seed crystal, beforenucleation on the SiO₂ mask, as a function of temperature.

DETAILED DESCRIPTION

Provided are methods for crystallizing amorphous multicomponent ioniccompounds (e.g., multicomponent oxides such as perovskite oxides,) whichhave been previously deposited on amorphous surfaces (e.g., a surface ofa plastic substrate), including in the form of intricate,three-dimensional structures.

By “multicomponent ionic compound” it is meant a chemical compoundcomprising a first type of cation, a first type of anion, and at leastone additional type of cation, at least one additional type of anion, orboth. Thus, binary ionic compounds composed of cations of a first typeand anions of a second type are not multicomponent ionic compounds.Rather, multicomponent ionic compounds include ternary compounds,quaternary compounds, etc. By way of illustration, a multicomponentionic compound may be a chemical compound composed of two types ofcations and one type of anion, three types of cations and one type ofanion, or one type of cation and two types of anions. The stoichiometryof the various cations and anions may vary in the compound, dependingupon the desired composition. In embodiments, the anions of the firsttype are oxygen anions such that the multicomponent ionic compound maybe referred to as a multicomponent oxide. In embodiments, themulticomponent oxide does not comprise any anions of a different type(i.e., it comprises only oxygen anions).

Illustrative multicomponent oxides include perovskite oxides (which mayalso be referred to as “perovskites”). Perovskite oxides include thosecharacterized by formula ABO₃. The valences of the A-site and B-sitecations have a sum of +6. The A-site and B-site cations may be selectedfrom various metallic elements. By way of illustration, the A-sitecations may be selected from alkaline earth elements, rare earthelements, and post-transition metal elements. B-site cations may beselected from transition metal elements (e.g., 3d transition metalelements) and post-transition metal elements. Specific illustrativeperovskite oxides include SrTiO₃, BaTiO₃, PbTiO₃, BaSnO₃, BiFeO₃, andLaAlO₃.

Perovskite oxides which exhibit layered structures upon crystallizationmay also be used. By way of illustration, perovskite oxides whichexhibit a Ruddlesden-Popper phase upon crystallization may be used. Someof the compounds within this series are characterized by formula(A_(1-x)A′_(x))₂BO_(4±δ). The A-site and B-site cations may be selectedfrom various metallic elements as described above with respect toperovskite oxides. An illustrative example is (La_(1-x)Sr_(x))₂BO_(4±δ),where B is selected from Co, Ni and Cu.

Other illustrative multicomponent oxides include ferrites and spinels.Ferrites are compounds composed of iron oxide combined chemically withone or more additional metallic elements. Ferrites include compoundscharacterized by formula A^(n+)(FeO_(x))^(n−), wherein A is a metallicelement (e.g., a transition metal element or an alkaline earth element).Ferrites include compounds characterized by formula A²⁺(Fe_(x)O_(y))²⁻where A is any divalent metallic ion. Many spinels are ferrites,including NiFe₂O₄, MnFe₂O₄, and CoFe₂O₄. Other specific illustrativeferrites include BaFe₂O₁₉ and SrFe₁₂O₁₉. Other spinels include thosecharacterized by formula AB₂O₄(see above) as well as those characterizedby formula ABCO₄. The A-site, B-site, and C-site cations may be selectedfrom various metallic elements as described above with respect toperovskite oxides. Another specific illustrative spinel is ScAlMgO₄.

Other illustrative multicomponent oxides include pyrochlores.Pyrochlores are characterized by formula A³⁺ ₂B⁴⁺ ₂O₇ or A²⁺ ₂B⁵⁺ ₂O₇.Pyrochlores can also incorporate oxygen vacancies, leading to a chemicalformula A₂B₂O_(6+x), wherein x ranges between 0 and 1 and the valencesof the A-site and B-site cations are as indicated in the pyrochloreformulas above. The A-site, B-site cations may be selected from variousmetallic elements as described above with respect to perovskite oxides.Pyrochlores also include pyrochlore iridates characterized by formulaA₂Ir₂O₇. In embodiments, A is selected from a rare earth element, e.g.,selected from Pr, Nd, Eu, and Tb.

In each of the formulas described above, the A-site, B-site and C-sitesmay be occupied by more than one type of the respective cation. That is,the A-site may be occupied by more than one type of A-site cation (e.g.,a mixture of Sr²⁺ and Ba²⁺); the B-site may be occupied by more than onetype of B-site cation; and the C-site may be occupied by more than onetype of C-site cation.

Other illustrative multicomponent oxides include substitutional alloysof Al₂O₃ in which some Al cations are substituted with another metalliccation, some O anions are substituted with another anion, or both.

At least some embodiments of the present methods may be used to providecrystalline multicomponent ionic compounds having compositions which arenot possible with conventional crystallization techniques. Conventionalcrystallization techniques typically involve temperatures at whichatomic surface diffusion and mass transport leads to phasedecomposition/separation, thereby preventing formation of the desiredcomposition, i.e., the desired stoichiometry, or desired crystalstructure. Such conventional techniques include epitaxial growthtechniques in which deposition/crystallization occurs simultaneously,such as high temperature pulsed laser deposition (PLD), high temperaturemagnetron sputtering, and chemical vapor deposition (CVD). By way ofillustration, formation of crystalline pyrochlore iridates usingconventional epitaxial growth techniques is highly challenging due tothe low reactivity of metallic iridium and the volatility of iridiumperoxides. Compositional analysis of thin films grown in situ at hightemperatures by PLD from a stoichiometric Eu₂Ir₂O₇ target have revealedthe absence of Ir or significant Ir deficiency.¹⁰⁻¹² Other conventionaltechniques which separate deposition and crystallization make use ofrelatively low temperatures for deposition, but relatively hightemperatures for crystallization (including temperatures sufficient tomelt/liquefy the deposited material), including rapid thermal processingsuch as flash heating, laser annealing and congruent melting. Again, theatomic diffusion/mass transport at these higher temperatures can preventformation of the desired composition/crystal structure. This means thatthe as-deposited composition of the material will not be the same as thecrystallized composition.

By contrast, and as further described below, the present methods involvesignificantly lower temperatures, temperatures at which atomicdiffusion/mass transport is sufficiently suppressed to minimize and evenprevent phase decomposition/separation during deposition and, at leastin some embodiments, crystallization. In this way, a selectedcomposition can be deposited on the amorphous surface and thensubsequently crystallized, wherein the crystallized composition is thesame as the as-deposited composition (i.e., the selected composition).“The same” means “substantially the same” in recognition of the factthat there may be deviations of the stoichiometry of the crystallizedcomposition from the stoichiometry of the as-deposited/selectedcomposition, but that these deviations are so small that the propertiesof the crystallized composition are those consistent with thecrystallized form of a composition having the stoichiometry of theas-deposited/selected composition. The stoichiometry of the crystallizedcomposition may be determined via x-ray photoelectron spectroscopy(XPS), Rutherford backscattering spectrometry (RBS), or electron probemicroanalysis (EPMA).

As noted above, the multicomponent ionic compounds are amorphous priorto crystallization. By “amorphous” it is meant the non-crystalline,metastable arrangement of atoms within the multicomponent ionic compoundcharacterized by the lack of long-range order of the atomic components.By way of illustration, FIG. 1 illustrates the thermodynamics of thedifferent phases of silicon (Si), i.e., gas, liquid, amorphous andcrystalline, as a function of temperature. In this figure, “amorphousSi” is analogous to the present amorphous multicomponent ioniccompounds. The existence of the amorphous phase of the multicomponentionic compounds may be confirmed using standard X-ray diffraction andscattering techniques, including those described in the Example, below.The amorphous multicomponent ionic compounds may also be characterizedas being homogenous, by which it is meant that the stoichiometry of theas-deposited amorphous multicomponent ionic compound is the samethroughout the material. “The same” means “substantially the same”wherein “substantially” has a meaning analogous to the meaning describedabove.

A variety of techniques may be used to deposit amorphous multicomponentionic compounds on amorphous surfaces. Illustrative techniques includeatomic layer deposition (ALD), pulsed laser deposition (PLD) andmagnetron sputtering. As described above, the temperatures used duringdeposition are those at which atomic diffusion/mass transport aresufficiently suppressed to minimize and even prevent phasedecomposition/separation of the selected multicomponent ionic compound.In embodiments, the temperature is less than the melting temperature ofthe selected amorphous surface, as further described below. Inembodiments, the temperature is less than about 300° C. This includesembodiments in which the temperature is less than about 250° C., lessthan about 200° C., less than about 150° C., less than about 100° C.,less than about 50° C., or even room temperature (i.e., from about 20 to25° C.).

The ALD technique provides compositional and chemical versatility aswell as extreme conformality, allowing for uniform deposition overhighly irregular shapes. Parameters for using ALD to provide amorphousmulticomponent ionic compounds, including single phases, alloys, andmulti-phase mixtures, may be found in, or adapted from, the following(each of which is incorporated by reference in its entirety):Miikkulainen et al., J. Appl. Phys. 113, 021301 (2013);¹³ Laskar et al.,ACS Appl. Mater. Interf. 8, 10572 (2016);¹⁴ Vehkamaki et al., Chem.Vapor. Dep. 7, 75 (2001);¹⁵ Hwang et al., J. Electrochem. Soc. 154, G69(2007);¹⁶ and Marchand et al., J. Phys. Chem. C 120, 7313 (2016).

The PLD and magnetron sputtering techniques also allow the creation ofmaterials with highly precise control of the metal ion composition. Byway of illustration, co-sputter deposition or PLD using a A₂Ir₂O₇ target(wherein A is selected from lanthanide or rare earth elements) and an Irtarget may be used to provide amorphous Ln₂Ir₂O₇. The flux control ofthe additional Ir source allows precise control of the composition ofthe as-deposited material. Parameters for using magnetron sputtering toprovide amorphous multicomponent ionic compounds are further describedin the Example, below. The composition of the amorphous multicomponentionic compound deposited by sputtering or PLD can be selected bychoosing the composition of the material used as the target in thesputtering or PLD sources and by adjusting deposition parameters such asbackground gas pressure, sputtering RF power, or PLD optical fluence.Amorphous perovskite oxides, e.g. SrTiO₃, can be deposited byradiofrequency (RF) sputtering of a stoichiometric target onto asubstrate held at room temperature using appropriate gas environments,for example a mixture of appropriate Ar and oxygen.¹⁷

The deposition step provides a layer of the amorphous multicomponentionic compound on the amorphous surface. The thickness of theas-deposited material is not particularly limited. The thickness of theas-deposited material refers to the dimension of the as-depositedmaterial as measured from the upper surface of the as-deposited materialto the upper surface of the amorphous surface, along an axis normal tothe amorphous surface. In embodiments, the thickness is at least about 5nm, at least about 10 nm, at least about 20 nm, at least about 50 nm, atleast about 75 nm, at least about 100 nm, at least about 150 nm, atleast about 200 nm, at least about 250 nm, or at least about 500 nm. Theother dimensions of the as-deposited material, i.e., those measuredparallel to the amorphous surface, are also not particularly limited.However, these other dimensions may be significantly greater than thethickness of the as-deposited material, e.g., a 100 nm-thick layer ofamorphous multicomponent ionic compound having a width and length on theorder of microns or centimeters. Thus, the shape of the as-depositedmaterial, i.e., as seen from a top, plan view, is not particularlylimited. In addition, the as-deposited material may be patterned usingstandard lithographic techniques into a variety of shapes as desired,prior to crystallization.

The amorphous surface onto which the amorphous multicomponent ioniccompound is deposited is provided by a deposition substrate. By“amorphous surface” it is meant a non-crystalline surface characterizedby the lack of long-range order. Epitaxial growth is not possible fromsuch amorphous surfaces. As illustrated in FIGS. 2A-2B (showing aside-view), a deposition substrate 200 has an upper surface 202(emphasized by a dotted line) which forms the interface with theas-deposited amorphous multicomponent ionic compound 204. In theembodiment shown in FIG. 2A, the upper surface 202 of the depositionsubstrate 200 defines a single region, i.e., the amorphous surface ontowhich an amorphous multicomponent ionic compound 204 is deposited. Thismay be accomplished by using deposition substrates composed of anamorphous material. A variety of amorphous materials may be used, e.g.,silica, other oxides or other glasses.

In embodiments, the amorphous material is an amorphous plastic.Illustrative amorphous plastics include polysulfone, polyimide,polyetherimide, polyethersulfone, polyarylsulfone, polyarylethersulfone,polycarbonate, polyphenylene oxide, polyphenylene ether, thermoplasticpolyurethane, acrylic, polystyrene, acrylonitrile butadiene styrene,polyvinyl chloride, polyethylene terephthalate, cellulose acetatebutyrate, and polytetrafluoroethylene.

In embodiments, the amorphous material (e.g., an amorphous plastic) ischaracterized by a melting temperature of about 400° C. or less. Thisincludes embodiments in which the amorphous material is characterized bya melting temperature of about 300° C. or less, about 250° C. or less,about 200° C. or less, or about 150° C. or less. This includesembodiments in which the amorphous material is polyimide characterizedby a melting temperature of about 400° C. or less; polyethyleneterephthalate characterized by a melting temperature of about 300° C. orless; polyetherimide, polyethersulfone, polystyrene or cellulose acetatebutyrate, each characterized by a melting temperature of about 250° C.or less; polysulfone, polyarylsulfone, polyarylethersulfone or acrylic,each characterized by a melting temperature of about 200° C. or less; orpolycarbonate, polyphenylene oxide, polyphenylene ether, thermoplasticpolyurethane, acrylonitrile butadiene styrene or polyvinyl chloride,each characterized by a melting temperature of about 150° C. or less.

In other embodiments such as the embodiment shown in FIG. 2B, the uppersurface 202 (emphasized by a dotted line) of the deposition substrate200 defines a plurality of regions 206 a-d. Then, the amorphous surfaceonto which the amorphous multicomponent ionic compound 204 is depositedis just one of the regions of the plurality of regions 206 a-d. Theplurality of regions 206 a-d may include crystalline surfaces (e.g., 206a and 206 c) in addition to amorphous surfaces (e.g., 206 b and 206 d).The amorphous surfaces 206 b, 206 d may be provided via an amorphousmaterial 201 (e.g., an amorphous plastic), while the crystallinesurfaces 206 a, 206 c may be provided via a crystalline material 203 onthe upper surface of the amorphous material 201. The depositionsubstrate 200 comprises the amorphous material 201 and the crystallinematerial 203.

Another embodiment of a deposition substrate 300 defining a plurality ofregions is illustrated in FIG. 3 (showing a side-view). Crystallinesurfaces of the plurality of regions may be provided by depositingand/or patterning an amorphous material 301 on the upper surface of acrystalline material 303 a. A crystalline surface may be provided via anexposed region 305 of the underlying crystalline material 303 a. Othercrystalline surfaces may also be provided by crystalline material 303 b,303 c deposited onto the overlying amorphous material 301. In eithercase, as further described below, the crystalline surfaces providecrystalline seeds or templates from which SPE growth into the amorphousmulticomponent ionic compound 304 can proceed (illustrated via thearrows/shading). The amorphous surfaces provided by the amorphousmaterial 301 provide a mask over which nucleation within the amorphousmulticomponent ionic compound 304 can be minimized and even preventedduring the SPE growth. Finally, FIG. 3 also shows that anothercrystalline material 303 d may be deposited onto the amorphousmulticomponent ionic compound 304 after deposition, prior tocrystallization. The deposition substrate 300 comprises the crystallinematerial 303 a-c and the amorphous material 301.

The crystalline material of the deposition substrates may be asingle-crystalline material, thereby providing single-crystallinesurfaces. The composition of the crystalline material may be selecteddepending upon the selected composition of the multicomponent ioniccompound. In embodiments, the compositions are the same, i.e., thecrystalline material is the multicomponent ionic compound in acrystalline phase. In embodiments, the compositions are not the same,but the compositions are lattice-matched. “Lattice-matched” means“substantially lattice-matched” wherein in “substantially” has a meaninganalogous to the meaning described above.

After deposition of the amorphous multicomponent ionic compound,crystallization is accomplished by applying an external stimulussufficient to induce an amorphous-to-crystalline phase transformation toconvert the amorphous multicomponent ionic compound to a crystallinephase. This amorphous-to-crystalline phase transformation may be adirect phase transformation, i.e., as opposed to indirectamorphous-to-liquid-to-crystalline phase transformations induced byrapid thermal processing using temperature sufficiently high tomelt/liquify the amorphous material. The term “crystallization” refersto the complete conversion of the amorphous phase to the crystallinephase. “Complete conversion” means “substantially complete conversion”wherein “substantially” has a meaning analogous to the meaning describedabove. As further described below, the mechanism by whichcrystallization is accomplished in the present methods can vary, e.g.,crystallization via SPE growth versus crystallization via nucleation. Inembodiments, crystallization is accomplished only via SPE growth.

A variety of external stimuli may be used, including thermal,mechanical, or combinations thereof. Thermal stimulus includes heatingthe amorphous multicomponent ionic compound to a temperature sufficientto induce the phase transformation. The heating may be accomplishedvarious ways, including by using an oven or a furnace. Selection of thetemperature is further described below. In at least some embodiments,the heating is uniform throughout the amorphous multicomponent ioniccompound, i.e., as opposed to heating localized to distinct regions inthe amorphous multicomponent compound. In other embodiments, the heatingmay be localized as when using lasers or high intensity lamps.

Mechanical stimulus includes applying a mechanical force to theamorphous multicomponent ionic compound. Mechanical force can be appliedby deforming (e.g., via bending, rolling, etc.) the amorphousmulticomponent ionic compound or the deposition substrate on which it isdeposited. In an illustrative embodiment, a scanning probe microscope(SPM) tip can be used to mechanically write nanoscale crystallineregions on the surface of the amorphous multicomponent ionic compoundupon the application of a very high vertical tip force, followingprocedures described for the crystallization of poly(ethylene oxide)melt droplets.¹⁸ Electron-beam-induced crystallization can be inducedusing a beam of electrons focused within the region of anamorphous-crystalline interface.¹⁹ The crystallization induced by theelectron beam proceeds from the amorphous-crystalline interface.

Various considerations (or combinations thereof) guide selection of thetemperature used to provide the thermal stimulus or the temperature usedduring other stimuli. In the Example, below, which uses thermalstimulus, the temperature is referred to as the annealing temperature.In some embodiments, the temperature is selected to suppress atomicdiffusion/mass transport in the amorphous multicomponent ionic compound,thereby minimizing or even preventing phase decomposition/separation.This is useful for ensuring that the composition of the crystallizedmulticomponent ionic compound is the same as the composition of theas-deposited amorphous multicomponent ionic compound and/or that thedesired crystal structure is achieved, as described above.

In some embodiments, the temperature is selected to minimize or evenprevent nucleation in the amorphous multicomponent ionic compound. Theterm “nucleation” refers to the self-assembly of the atomic componentsof the amorphous multicomponent ionic compound into a larger arrangementof atoms characteristic of a crystalline phase, from which arrangementcrystallization can proceed. The term refers to both homogenousnucleation (i.e., occurring within the bulk of the amorphousmulticomponent ionic compound) and heterogeneous nucleation (i.e.,occurring at an interface between the amorphous multicomponent ioniccompound and an amorphous surface). The term is distinguished fromcrystallization via SPE growth from a crystalline surface. Selection ofthe temperature to minimize/prevent nucleation is useful for embodimentsinvolving crystallization over a deposition substrate having bothamorphous and crystalline surfaces or when the amorphous multicomponentionic compound is otherwise in contact with a crystalline surface (e.g.,via a seed/template of a crystalline material 303 d as shown in FIG. 3).In such embodiments, the temperature may be selected to achievecrystallization via SPE growth from the crystalline surface withoutnucleation. “Without” means “substantially without” wherein“substantially” has a meaning analogous to the meaning described above.Such embodiments are based, at least in part, on the inventors' findingthat the activation energy of nucleation of an amorphous material overan amorphous surface is significantly higher than the activation energyof SPE growth of the amorphous material from a crystalline surface. Thisfinding is further described in the Example, below.

The temperature which induces crystallization via SPE growth withoutnucleation depends upon the selected composition of the amorphousmulticomponent ionic compound, the deposition technique and conditionsused to form the amorphous multicomponent ionic compound, and the amountof the as-deposited material to be crystallized via SPE growth from thecrystalline surface before competing polycrystalline nucleationprocesses occur. The amount may be quantified as the distance asmeasured from the crystalline/amorphous interface (from which SPE growthproceeds) to an oppositely facing surface of the amorphousmulticomponent ionic compound.

For a selected composition of the amorphous multicomponent ioniccompound (and deposition technique/conditions), the maximum distancethat can be crystallized via SPE growth without nucleation increases asthe temperature decreases. This maximum distance is also referred to asthe “maximum crystallization distance before nucleation L_(C)” in theExample below. FIG. 12B shows the variation of L_(C) forsputter-deposited SrTiO₃ as a function of temperature. The techniques inthe Example, below, may be used to determine L_(C) as a function oftemperature for a particular composition and depositiontechnique/conditions. Then, the temperature can be selected based upon agiven distance associated with the as-deposited amorphous multicomponentionic compound to be crystallized.

Other considerations which may guide selection of the temperatureinclude preventing the melting of the selected amorphous multicomponentionic compound. Thus, the temperature may be less than the meltingtemperature of the selected amorphous multicomponent ionic compound.This distinguishes crystallization techniques using temperatures whichare sufficiently high to liquefy/melt portions of an amorphous material,as described above. Moreover, this distinguishes crystalline techniquesinvolving indirect amorphous-to-liquid-to-crystalline phasetransformations. The temperature may be less than the meltingtemperature of the selected amorphous surface, which may be a relativelylow melting temperature amorphous plastic as described above.

Illustrative temperatures include temperatures of about 1200° C. orless, about 1000° C. or less, about 800° C. or less, about 600° C. orless, about 550° C. or less, about 500° C. or less, about 450° C. orless, or about 400° C. or less. This includes embodiments in which thetemperature is in the range of from about 400° C. to about 600° C., orfrom about 400° C. to about 500° C. In some embodiments, e.g., whenusing mechanical stimuli, the temperature may be about room temperature.

As noted above, crystallization of the amorphous multicomponent ioniccompound provides the multicomponent ionic compound in a crystallinephase. The crystalline phase may be a single-crystalline phase or apolycrystalline phase. The single-crystalline phase may be achieved byusing single-crystalline surfaces from which SPE growth can occur. Bycontrast, crystallization via nucleation results in a polycrystallinephase. The term “polycrystalline” is distinguished from a mixedamorphous-polycrystalline phase.

Compared to conventional crystallization techniques which are generallyconstrained to planar two-dimensional 2D structures, the dimensionalityand morphology of the crystallized multicomponent ionic compoundsprovided by the present methods is not particularly limited. Standardthin film deposition and lithographic techniques may be used to providedeposition substrates having a variety of surface morphologies andsurface regions. By way of illustration, at least some embodiments ofthe present methods may be used to achieve three-dimensional (3D)structures composed of crystalline multicomponent ionic compounds,including structures having intricate geometries with nanoscaledimensions (e.g., dimensions on the order of 100s or 10s of nanometers).

One such embodiment is illustrated in FIGS. 4A-4D. FIG. 4A shows aside-view of a deposition substrate 400 comprising a single-crystallinematerial 403. Standard thin film deposition and lithographic techniquesmay be used to create a two-dimensional (2D) structure (left) and a 3Dstructure (right), each composed of an amorphous material 401, on theupper surface of the single-crystalline material 403. “2D” is used torefer to structures best characterized by two dimensions x and y, e.g.,a width and length. (See the axis in FIG. 4A, where they axis isperpendicular to the plane of the page.) 2D structures may have a thirddimension z (e.g., height), but generally z<<x, y. The other twodimensions x, y may be of similar magnitude. “3D” is used to refer tonon-planar structures best characterized by three dimensions x, y and z,each which may be of similar magnitude. In both cases, these dimensionsmay refer to the overall dimensions of the structure since both 2Dstructures and 3D structures may include lower dimensional featureswithin the structures. By way of illustration, the 3D structure of FIG.4A includes lower dimensional, e.g., one-dimensional channels or 2Dshelves. Thus, the upper surface of the deposition substrate 400 of FIG.4A is non-planar and three-dimensional defining a plurality of regionsincluding both amorphous surfaces and single-crystalline surfaces. Adeposition substrate having one or more 3D structures thereon may bereferred to as a 3D deposition substrate.

Next, as illustrated in FIG. 4A, a low-temperature deposition techniquesuch as ALD may be used to coat the deposition substrate 400 having theplurality of regions with an amorphous multicomponent ionic compound404. As described above, ALD is useful to provide a conformal coatingeven in the channels/shelves of the 3D structure. FIGS. 4B and 4Cillustrate the process of heating the as-deposited amorphousmulticomponent ionic compound 404 to a temperature sufficient to achievecrystallization via SPE growth from the crystalline surfaces of thedeposition substrate 400 without nucleation within the amorphousmulticomponent ionic compound 404. The SPE growth is illustrated withhatching.

The largest distance d of the amorphous multicomponent ionic compound404 to be crystallized via SPE growth (see FIG. 4A) may be used toselect the appropriate temperature as described above. This largestdistance may effectively be a SPE crystallization pathway which proceedsfrom an amorphous-crystalline interface along more than one direction.By way of illustration, in the embodiment of FIG. 4A, the longest SPEcrystallization pathway is labeled with arrows. Thus, the largestdistance d is z+x and the temperature may be selected such thatL_(C)≥z+x. Finally, as shown in FIG. 4D, selective etching may be usedto remove the amorphous 2D and 3D structures, thereby resulting in asingle-crystalline multicomponent ionic compound 408 having a complex,3D geometry.

FIG. 3 also illustrates that standard transfer techniques may be used inthe present methods to transfer the crystalline material 303 b-c todesired locations on the deposition substrate 300 or on the uppersurface of the amorphous multicomponent material 304, further increasingthe scope of possible dimensionalities and morphologies for theresulting crystalline multicomponent ionic compounds. By way ofillustration, single crystals having a variety of sizes (e.g.,micron-to-millimeter sizes) can be lifted from the substrate on whichthey are crystallized by using polydimethylsiloxane (PDMS) orpolymethylmethacrylate (PMMA) layers as stamps.^(20,21) Anotherillustrative transfer process involves suspending an oxide singlecrystal at the surface of water or of an aqueous solution and thentransferring it to a new substrate.²² Both techniques allow the singlecrystals to be transferred to the amorphous substrate of interest inorder to establish intricate patterns or to serve as seed crystals.

The present methods may also be used to provide heterostructurescomprising interfaces between different crystalline multicomponent ioniccompounds. By way of illustration, a bilayer comprising a first layer ofa first amorphous multicomponent ionic compound and a second layer of asecond amorphous multicomponent ionic compound on the first layer may bedeposited and subsequently crystallized as described above. More thantwo layers of different amorphous multicomponent ionic compounds may beused to provide multilayer heterostructures. The appropriate layeredstructures can be created by depositing the layers of amorphousmulticomponent ionic compounds sequentially using the depositionprocedures previously described. There are several potentialapplications of interfaces created by the crystallization ofmulticomponent ionic materials. The composition of the first and secondmulticomponent ionic compounds may be selected to support a 2DEG or 2DHGat the resulting interface under the application of an electric field.Additionally, the multilayer heterostructure can incorporateferroelectric and dielectric components such as PbTiO₃ and SrTiO₃,respectively, and can be crystallized to form superlattices ormultilayers with ferroelectric functionality. The interfaces of themultilayer heterostructure can be constructed to have structuralfeatures promoting ferroelectricity due to interface rotations of oxygenoctahedra.²³ Lithographic patterning techniques, includingphotolithography, electron-beam lithography, focused ion-beamlithography, or nanoimprint lithography may be employed to pattern thelayers of the multicomponent ionic compounds either before (in theamorphous form) or after crystallization, which may be useful to providelower dimensional structures such as one-dimensional (1D) wires andzero-dimensional (0D) dots.

Transfer techniques such as those described above may also be used inthe present methods to release and transfer layers of the multicomponentionic compounds either before (in the amorphous form) or aftercrystallization. The substrates to which the layers of themulticomponent ionic compounds are transferred may be referred to astransfer substrates. A variety of transfer substrates may be used,depending upon the desired application. Transfer substrates include avariety of semiconductors such as silicon. This is useful forintegrating the electronic, ferroelectric, magnetic, or multiferroic,functionalities of the crystalline multicomponent ionic compounds intocomplementary metal oxide semiconductor (CMOS) circuitry. Transfertechniques may also be used to form multilayer structures of differentcrystalline multicomponent ionic compounds, i.e., multiple individuallayers of amorphous multicomponent compounds may be crystallized asdescribed above and then released and stacked to form a multilayerstructure.

In addition to those described above, the crystalline multicomponentionic compounds provided by the present methods find use in a variety ofother applications, e.g., transparent multicomponent oxides for use inoptoelectronic devices and piezoelectric multicomponent oxides for usein acoustic and strain transduction. Crystalline multicomponent ioniccompounds may also be used as epitaxial growth substrates for othermaterials, including challenging materials such as GaN, ZnO alloys,BaSnO₃, as well as other semiconductors and electronic materials.

The present disclosure also encompasses the crystalline multicomponentionic structures formed using the present methods, including thecrystalline multicomponent ionic structures configured as intricate, 3Dstructures. Devices including the crystalline multicomponent ionicstructures are also encompassed.

EXAMPLE

Introduction

This Example reports the relative rates of nucleation and growth in thecrystallization of SrTiO₃ (STO). STO serves as a model for perovskitesystems of interest and has experimental advantages arising from itssimple-cubic symmetry and lack of competing structural phases of thesame stoichiometry. The growth kinetics of STO are applicable to theformation of structurally similar crystalline oxides on varioussubstrates and geometries. In addition, STO itself has a range offunctionalities, including as a high-k gate insulator in field effecttransistors,⁹ a nanoscale ferroelectric,¹⁰ and through formation of2DEGs at LaAlO₃/SrTiO₃ (LAO/STO) interfaces.⁸ The crucial insight thatarises from comparing the rates of nucleation and growth is that thereis a difference in the kinetics of crystallization of amorphous STO thinfilms on two substrates: single-crystal (001) STO and SiO₂/(001) Si.This Example provides a thorough study of the kinetics ofcrystallization of amorphous STO and enables synthesizing single-crystalSTO in complex geometries.

The nucleation and growth of crystalline STO from initially amorphouslayers were investigated using a two-step experimental procedure: (i)sputter deposition of amorphous STO thin films on room temperaturesubstrates and (ii) crystallization via post-deposition ex-situannealing. The amorphous-to-crystalline transformation is dramaticallydifferent on the two substrates, as shown schematically in FIGS. 5A and5B. As shown in FIG. 5A, on the STO substrate the initially amorphouslayer crystallizes via SPE as an epitaxial thin film. As shown in FIG.5B, the SiO₂/(001) Si substrates do not provide a well-defined epitaxialrelationship and thus the eventual crystallization of amorphous STOlayers deposited on SiO₂ produces a nanocrystalline STO.

The crystallization of STO on (001) STO substrates occurs through SPEvia the motion of the amorphous/crystalline interface towards thesurface.¹¹ The kinetics of SPE in STO have been studied in amorphouslayers created by ion implantation,¹¹⁻¹² sputter deposition,¹³ andpulsed-laser deposition.¹⁴ In addition to STO, crystallization by SPEhas also been demonstrated in other complex oxides, for example in theperovskites EuTiO₃,¹⁵ CaTiO₃,¹¹ and BiFeO₃ on STO.¹⁶⁻¹⁷SPE inhomoepitaxial STO is similar to the widely employed methods in thecrystallization of elemental semiconductors and SiGe semiconductoralloys.¹⁸ The interface velocity observed in the crystallization of STOby SPE depends on sample preparation, with higher velocities observed inamorphous layers prepared by ion implantation than in layers prepared bysputter deposition.^(11, 13) The growth velocity also depends onimpurities and can be increased significantly by increasing the Hconcentration within the oxide layer by crystallization in an atmospherewith a high H₂O partial pressure.^(12, 19)

The crystallization of amorphous STO layers deposited on SiO₂/(001) Si,in contrast with SPE, occurs through crystal nucleation far from theinterface. Nucleation involves a set of atomic-scale processesassociated with the rearrangement of the nanometer scale structure intolocal metal-oxygen coordinations favorable for crystal formation.²⁰These processes differ from the crystal-interface-dependent atomicprocesses of growth and thus nucleation has a distinct activationenergy.

This Example finds that there is a regime of temperatures in which thenucleation of crystalline STO from amorphous STO is exceedingly slowcompared to growth proceeding from a STO crystal substrate. Thetemperature dependence of nucleation and growth processes for amorphousSTO shows that the nucleation of STO on SiO₂/Si occurs with a higheractivation energy than for the velocity of the crystal/amorphous STOinterface. The low-temperature range is important because it is at thelow temperatures where the rates of crystal growth for STO on STO andnucleation for STO on SiO₂/Si are significantly different. Theappropriate control of nucleation rates, coupled with amorphous STOdeposition, is the key in creating single-crystal films inunconventional geometries.

Methods

STO substrates were purchased from Shinkosha Co., Ltd, with one sidepolished. In order to prepare TiO₂ terminated substrates before growth,STO crystals were prepared with annealing and deionized (DI) watertreatment.²⁶⁻²⁷ The substrate preparation was a three-step process thatconsisted of annealing at 1000° C. for 1 h, sonicating the substrates inDI water to dissolve superficial strontium oxide that resulted from thefirst anneal, and annealing for a second time at 1000° C. for 1 h. TheSTO substrates were then sonicated with acetone, isopropyl alcohol(IPA), methanol and DI water, with 2 minutes in each solvent. Unlike theSTO substrates, the SiO₂/(001)Si substrates were not subjected toadditional processing steps prior to cleaning.

Prior to depositing the amorphous STO films, the chamber was evacuatedto 2×10⁻⁶ Torr. STO layers were grown with the substrate at roomtemperature at a total pressure of 18 mTorr with an Ar:O₂ flow-rateratio of 6:1.

High-resolution TEM imaging was conducted using a Tecnai TF-30transmission electron microscope operated at 300 keV. Thehigh-resolution images for STO grown on SiO₂/(001)Si substrate wereobtained for the Si (110) cross-sectional plane, while images for STO on(001) STO substrate were obtained for the STO (100) cross-sectionalplane.

Grazing incidence x-ray diffraction was carried out to characterize thecrystalline nature of the thin films, using a Bruker D8 Advancediffractometer with Cu Kα radiation at a wavelength of 1.54 Å, at a tubevoltage 50 kV and current 1 mA. The scattered intensity was recordedusing a two-dimensional x-ray detector. The incidence angle of the x-raybeam was determined by the beam width and sample size, to optimize theamorphous peak signal by maximizing the footprint of x-ray on samples.The incident angles for STO on STO and STO on SiO₂/Si were 3.2° and1.4°, respectively. The detector angles of all measurements were fixedat 30°. XRR data were collected using a Panalytical X'Pert MRD withmonochromatic Cu Kα1 x-ray radiation with a wavelength of 1.5406 Å.

Results

Amorphous STO films were deposited by on-axis RF magnetron sputterdeposition onto substrates held at room temperature. Films weredeposited at a growth rate of 15 nm h⁻¹ with total thicknesses ofapproximately 60 nm. The thickness of each as-deposited film thicknesseswas measured using XRR. The as-deposited STO layers on both STO andSiO₂/Si substrates exhibited grazing incidence x-ray scattering patternsconsistent with an amorphous thin film. FIGS. 6A and 6B show x-rayscattering patterns of amorphous STO films deposited under the sameconditions on STO and SiO₂/Si substrates, respectively. A slightdifference in the intensities of the scattering patterns in FIGS. 6A and6B arises from the different incident angle of x-ray beam chosen formeasurements of STO on STO (3.2°) and STO on SiO₂/Si (1.4°).

For STO on the (001) STO substrate, heating the sample induced acrystallization process in which the amorphous scattering signaldisappeared without the appearance of polycrystalline diffraction rings.FIG. 6C shows the x-ray scattering pattern of an STO film with anas-deposited thickness of 61 nm after annealing at 650° C. for 5 min.TEM provides further evidence of the crystallization of STO on STO bySPE. Annealing an as-deposited amorphous film at 600° C. for 32 minresults in a single-crystal epitaxial STO layer, as shown by the TEMimage in FIG. 7A. The image was obtained for the STO (100)cross-sectional plane. The orientation of the lattice fringes in FIG. 7Ais consistent throughout the entire structure and identical to thesubstrate, as seen on the magnified section in the right panel of FIG.7A. These observations are consistent with the expectation that thecrystallization of STO on STO occurs via SPE.

For STO on SiO₂/(001) Si, heating transforms the amorphous layer into ananocrystalline microstructure. FIG. 6D shows the x-ray scatteringpattern of a crystallized STO thin film after annealing at 650° C. for18 min, exhibiting a series of powder diffraction rings arising from(100), (110) and (111) reflections of STO. The integrated intensity of(100) and (111) peaks are 3.3% and 19.8% of the intensity of the (110)peak, respectively. The peak positions and ratios of peak intensitiesagree with the powder x-ray diffraction pattern of STO,²¹ furtherconfirming that polycrystals of STO form on SiO₂/(001) Si in randomorientations. The crystal size determined from the angular widths of the(100), (110) and (111) reflections is 11 nm, 7 nm and 6 nm,respectively, based on Scherrer's formula. The size of the STO crystalsis much smaller than the film thickness, indicating that STO crystalnucleation occurs within the bulk of the film and is not limited to thefree surface or the STO/SiO₂ interface.

The crystallized STO layer and SiO₂/(001) Si substrate are shown in theTEM image in FIG. 7B for an STO layer with an initial thickness of 61 nmheated to 600° C. for 36 min. The image was obtained for the Si (110)cross-sectional plane. A high-resolution image of one of thenanocrystals within the layer exhibits lattice fringes with amisorientation of 11° with respect to the Si substrate. Other domainscontaining (110) crystal planes, with different angular orientationswith respect to Si, were also observed in the HRTEM analysis. Thespacing of the lattice planes in the polycrystalline domain shown inFIG. 7B is 2.76 Å, corresponding to the STO (110) plane. An interfacialoxide is also apparent in FIG. 7B. The growth of amorphous STO onSiO₂/(001)Si has been shown to facilitate an initial thickening of theinterfacial SiO₂ layer due to oxidation of the silicon substrate.¹⁴

The dependence of the scattered x-ray intensity for an amorphous STOlayer on (001) STO for a series of crystallization times at 600° C. wasobtained. Data was acquired in a series of separate heating steps, eachof which was followed by x-ray scattering characterization. Theintensity of scattering from the amorphous layer gradually decreaseswith increasing annealing time. The integrated amorphous phase scatteredx-ray intensity is shown as a function of heating time for a wide rangeof annealing temperatures in FIG. 8A. The details of the determinationof the amorphous phase scattered x-ray intensity from 2D detector imagesis given in the Methods section. The intensity in the angular range ofscattering from the amorphous layer is slightly higher than thebackground even following long annealing times, an effect that isaccounted for in the analysis below. It is hypothesized that this smalldifference, which is on the order of 10-30% of the total intensity ofthe scattering from the amorphous layer, may arise from smalldifferences in the run-to-run alignment of the sample on the x-raydiffractometer, the formation of very small crystallites, or scatteringfrom surface contamination accumulated during processing.

The growth velocity for crystallization of STO on (001) STO via SPE wasdetermined from the rate of decrease of the scattered x-ray intensityfrom the amorphous layer. The amorphous phase scattered x-ray intensity,I, can be modeled as I=C x(t)+ΔI. Here, C is a constant dependent on theincident x-ray intensity, the scattering per unit volume from theamorphous layer, and detector parameters, x(t) is the thickness of theamorphous layer at time t, and ΔI is the non-zero scattered x-rayintensity of the fully crystallized film. The velocity is

$v = {\frac{dx}{dt} = {\frac{1}{C}{\frac{dI}{dt}.}}}$

The constant C can be obtained by comparing the initial state and finalstates,

${C = \frac{I_{0} - {\Delta \; I}}{x_{0}}},$

where x₀ is the initial thickness of the amorphous STO film and I₀ isthe initial scattered intensity of the as-deposited film. The growthvelocity, v, is then given by:

$\begin{matrix}{v = {\frac{d\; I}{dt}\frac{x_{0}}{I_{0} - {\Delta \; I}}}} & (1)\end{matrix}$

The growth velocities found by applying equation (1) to the x-ray dataare plotted as a function of temperature in FIG. 8B. The velocitiesrange from 0.6 nm min⁻¹ at 450° C. to 12.3 nm min⁻¹ at 650° C. Themeasured velocity of 2 nm s⁻¹ at 500° C. is similar to the value of 4 nms⁻¹ that can be inferred from a previous report of the time required tocrystallize a sputter-deposited STO film at the same temperature.¹³

Previous studies of SPE of STO, as well as in Si, SiGe and othersemiconductors have found that the growth velocity is described by anArrhenius temperature dependence given by v(T)=v₀e^(−E) ^(a) ^(/k) ^(B)^(T). Here Ea is the effective activation energy for the processesdetermining the velocity, v₀ is a prefactor with units of velocity,k_(B) is the Boltzmann constant, and T is the temperature. A fit of thisexpression to the growth velocities reported in FIG. 8B for thetemperature range from 450° C. to 650° C. gives an activation energy of0.7 eV.

Reported activation energies for the growth front velocity forcrystallization of STO on STO substrates varies significantly dependingon the gas ambient during annealing.^(12, 19) The activation energyobtained in this Example is in reasonable agreement with the value of0.77 eV reported for ion-implanted amorphous STO by SPE in the (100)direction.¹¹ Other reported activation energies range from 1.2 eV in anH₂O atmosphere to more than 3 eV in vacuum.¹² The impact of this rangeof activation energies on the finding of the temperature dependence ofthe relative rates of nucleation and growth is discussed in more detailbelow.

XRR provides further support for the crystallization of STO on (001) STOby the motion of a planar crystal/amorphous interface by SPE. XRR curvesfor an amorphous STO layer on a STO substrate were obtained for a seriesof annealing times at 600° C. Amorphous layer thicknesses determinedfrom the average fringe spacing decrease continuously as a function oftime, as shown in FIG. 9. The velocity determined from FIG. 9 is 1.1nm/min, slightly less than the growth velocity at 600° C., obtained fromthe intensity of the x-ray scattering data on a different sample asshown in FIG. 8A is 1.9 nm/min.

The crystallization of STO on SiO₂/(001) Si occurs by a polycrystallinenucleation and growth process. The time dependence of the intensity ofx-ray scattering from amorphous STO layers on SiO₂/Si at an annealingtemperature of 600° C. was examined. After annealing for 16 min,polycrystalline STO peaks start to appear, marking the point when alarge number of nuclei have formed. This nucleation time depends on thetemperature of the crystallization process. Without seed crystals ortemplates on the substrate, nuclei form in random orientations,resulting in polycrystalline film. An initial increase in scatteredamorphous intensity for annealing between 450 and 600° C. occurs beforethe appearance of crystalline x-ray reflections and could in principlearise from a rearrangement within the amorphous structure.

XRR curves for an STO layer deposited on SiO₂/(001) Si and annealed at600° C. for different time periods were obtained. For STO on SiO₂/(001)Si the fringe spacing provides information about the total STO filmthickness because the density difference between STO and SiO₂ is muchlarger than the density difference between crystalline STO and amorphousSTO. The total film thickness decreases slightly upon crystallization,from 46 nm to 40 nm, as shown in FIG. 10. FIG. 10 also shows the ratioof the density to the final density as a function of annealing time,based on the assumption that the total mass does not change. Theas-deposited density of amorphous STO phase is 87% of the density offinal crystalline STO, consistent with reported densities of 4.2±0.1 gcm⁻³ and 5.1 g cm⁻³ for amorphous and crystalline STO,respectively.^(12,22-23) The XRR results thus indicate that a densitychange of on the order of 13% can be expected during the crystallizationof amorphous STO.

FIGS. 11A-11D summarize the crystallization dynamics of STO for the twodifferent substrates by comparing the time-evolution of the intensity ofscattering from the amorphous STO layer. Two effects are apparent inthese figures. First, the crystallization of amorphous STO on STO occursin a much shorter time than that on SiO₂. Second, role of nucleation inthe crystallization of STO on SiO₂/Si can be quantified by consideringthe nucleation time t*, which is defined to be the longest time at whichamorphous phase scattered x-ray intensity is equal to its as-depositedvalue. The nucleation time, t*, for STO on SiO₂ is longer than thecrystallization time of STO on STO at lower annealing temperatures. Forinstance, at 450° C., t* is 14 h whereas the crystallization of STO onSTO (001) is completed in less than 1 h. The nucleation time at 650° C.is less than the minimum annealing time, and thus was not measured.

Assuming that the nucleation process is also thermally activated, thenucleation time t* for STO on SiO₂/Si can be expressed using anArrhenius temperature dependence:

$\frac{1}{t^{*}} = {\frac{1}{t_{0}^{*}}{e^{{{- E_{b}}/k_{B}}T}.^{40}}}$

Here 1/t₀* is a temperature-independent constant and E_(b) is theactivation energy for nucleation. The variation of t* with temperatureis plotted in FIG. 12A. The nucleation activation energy obtained byfitting the experimentally observed nucleation time with thistemperature dependence is 1.4 eV. The difference between the activationenergies for crystal growth and nucleation is a key effect that enablesfinding a window in which growth proceeds without significantnucleation.

Discussion

This relatively long nucleation time for STO on SiO₂ provides theinsight required to form STO and other complex oxides in sophisticatedgeometries. In such cases, crystalline STO can act as a crystallinetemplate and materials with other compositions, such as SiO₂, serve as amask. As is apparent from the long nucleation times in FIGS. 11A-11D,the SiO₂ mask can geometrically direct the crystallization path withoutproviding sites for crystallization. The key parameter for the processof guiding the path of crystallization using a mask is the maximum filmthickness or distance over which the amorphous STO can crystallizebefore the nucleation of crystalline STO occurs away from the movinginterface.

The SPE crystallization velocities and polycrystal nucleation time canbe used to deduce the maximum crystallization distance beforenucleation, L_(C). L_(C) can be expressed as L_(C)=vt*, where v is theSPE crystallization velocity on STO and t* is the nucleation time onSiO₂. The values of L_(C) at annealing temperatures in the range of thisExample are plotted in FIG. 12B. The distance covered before nucleationincreases as the temperature decreases. The largest distance is achievedat the relatively low temperature of 450° C. FIG. 12B indicates that fortemperatures above 600° C. the crystallization lengths that can beachieved are less than 50 nm, lower than the thickness of as-depositedamorphous layers. Crystallizing amorphous films by SPE at temperaturesabove 600° C. thus raises the possibility of creating highly defectivefilms due to nucleation away from the crystal-amorphous interface.

L_(C) is a function of v and t*, which were assumed to be both thermallyactivated. Therefore, L_(C) can be expressed as:

$\begin{matrix}{L_{C} = {{vt}^{*} = {{v_{0}t_{0}^{*}e^{- \frac{E_{a} - E_{b}}{k_{B}T}}} = {v_{0}t_{0}^{*}e^{- \; \frac{\Delta \; E}{k_{B}T}}}}}} & (2)\end{matrix}$

By fitting the data in FIG. 12B with Eq. (2), using W and ΔE as fittingparameters, the maximum film thicknesses at different annealingtemperatures can be estimated.

The increase in the crystallization distances at low temperaturesapparent in FIG. 12B shows that flash heating, or other rapid thermalprocessing techniques at high temperatures, are not appropriate forsuppressing nucleation to create thick single-crystalline layers of STO.A similar consideration is important in the crystallization of STOwithin high aspect ratio structures, e.g., narrow and deep trenches orpores. Very large distances of the progression of crystalline interfacesare obtained at low temperatures, e.g., 500 nm at 450° C. Equation (2)further suggests that L_(C) can be increased by further optimizing thedifference between the activation energies for nucleation and interfacemotion, for example by varying the gaseous environment around the sampleduring heating.

The observation that STO can be crystallized even in the presence ofpotential mask materials points to methods through which similarfunctional oxides, e.g., ferroelectric PbTiO₃ and BaTiO₃, can be grownin complex geometries. In addition, other complex oxide electronicinterfaces can be created by recrystallization, facilitating theintegration of complex oxides in 3D electronic and optoelectronicdevices. Low-energy ion bombardment and annealing of an LAO/STO 2DEGformed at the interface between a 4 nm-LAO thin film and STO substratelead to the disappearance and recovery of the 2DEG.²⁵

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The word “illustrative” is used herein to mean serving as an example,instance, or illustration. Any aspect or design described herein as“illustrative” is not necessarily to be construed as preferred oradvantageous over other aspects or designs. Further, for the purposes ofthis disclosure and unless otherwise specified, “a” or “an” means “oneor more”.

The foregoing description of illustrative embodiments of the inventionhas been presented for purposes of illustration and of description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed, and modifications and variations are possible inlight of the above teachings or may be acquired from practice of theinvention. The embodiments were chosen and described in order to explainthe principles of the invention and as practical applications of theinvention to enable one skilled in the art to utilize the invention invarious embodiments and with various modifications as suited to theparticular use contemplated. It is intended that the scope of theinvention be defined by the claims appended hereto and theirequivalents.

What is claimed is:
 1. A method for crystallizing an amorphousmulticomponent ionic compound, the method comprising applying anexternal stimulus to a layer of an amorphous multicomponent ioniccompound, the layer in contact with an amorphous surface of a depositionsubstrate at a first interface and optionally, the layer in contact witha crystalline surface at a second interface, wherein the externalstimulus induces an amorphous-to-crystalline phase transformation,thereby crystallizing the layer to provide a crystalline multicomponentionic compound, wherein the external stimulus and the crystallizationare carried out at a temperature below the melting temperature of theamorphous multicomponent ionic compound, and wherein, if the layer is incontact with the crystalline surface at the second interface, thetemperature is further selected to achieve crystallization from thecrystalline surface via solid phase epitaxial (SPE) growth withoutnucleation.
 2. The method of claim 1, wherein the amorphousmulticomponent ionic compound is an amorphous multicomponent oxide. 3.The method of claim 2, wherein the amorphous multicomponent oxide isselected from perovskites, spinels, pyrochlores, and ferrites.
 4. Themethod of claim 1, wherein the amorphous surface is provided by anamorphous plastic.
 5. The method of claim 1, further comprisingdepositing the layer of the amorphous multicomponent ionic compound onthe deposition substrate prior to crystallization.
 6. The method ofclaim 5, wherein the deposition is carried out at a temperature of about300° C. or less.
 7. The method of claim 1, further comprising releasingand transferring the layer of the crystalline multicomponent ioniccompound to a transfer substrate.
 8. The method of claim 7, wherein thetransfer substrate is a silicon substrate.
 9. The method of claim 1,wherein the layer of the amorphous multicomponent ionic compound is incontact with the crystalline surface at the second interface.
 10. Themethod of claim 9, wherein the external stimulus is a thermal stimuluscomprising heating the layer to the selected temperature.
 11. The methodof claim 10, wherein the selected temperature is such that a maximumcrystallization distance L_(C) at the selected temperature is greaterthan or equal to the largest distance to be crystallized via the SPEgrowth in the layer of the amorphous multicomponent ionic compound. 12.The method of claim 11, wherein the largest distance to be crystallizedis at least about 50 nm.
 13. The method of claim 11, wherein the largestdistance to be crystallized is at least about 100 nm.
 14. The method ofclaim 10, wherein the selected temperature is no greater than about 550°C.
 15. The method of claim 9, wherein the deposition substrate comprisesa plurality of regions, wherein the amorphous surface and thecrystalline surface are ones of the plurality of regions.
 16. The methodof claim 9, wherein the crystalline surface is a single-crystallinesurface and the crystallization provides a single-crystallinemulticomponent ionic compound.
 17. The method of claim 15, wherein thedeposition substrate is non-planar and three-dimensional such that thelayer of amorphous multicomponent ionic compound is characterized by acomplementary three-dimensional morphology and the crystallizationprovides the crystalline multicomponent ionic compound alsocharacterized by the complementary three-dimensional morphology.
 18. Themethod of claim 1, wherein the layer is not in contact with thecrystalline surface at the second interface.
 19. The method of claim 18,wherein the crystallization provides a polycrystalline multicomponentionic compound of the same composition as the amorphous multicomponentionic compound.
 20. The method of claim 19, wherein the amorphousmulticomponent ionic compound is a pyrochlore iridate.